Case-scale analysis

Pair-wise correlations

Age

Altitud

BMI

Diabetes

Hypertension

Sugar

Vitamin D

Multiple regression

Response variable = vit D
Explanatory variables = age, bmi, hypert, & diab

## 
## Call:
## lm(formula = vitD ~ Age + BMI + Hypert + Diab, data = d)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -47.910 -11.527  -0.912  10.282  86.768 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 77.80754    2.25265  34.540  < 2e-16 ***
## Age         -0.19993    0.04896  -4.083 4.59e-05 ***
## BMI         -0.32273    0.06663  -4.844 1.36e-06 ***
## Hypert1      0.99618    1.32710   0.751    0.453    
## Diab1       -1.43195    0.88457  -1.619    0.106    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.5 on 2205 degrees of freedom
## Multiple R-squared:  0.02937,    Adjusted R-squared:  0.02761 
## F-statistic: 16.68 on 4 and 2205 DF,  p-value: 1.785e-13

The explanatory variables, together, explain a negligible amount of the variance in Vit D (see R-squared). When controlling for the other variables, both age and BMI have a negative and signficiant relation with Vit D (see column "Pr(>|t|)").

Municipal-scale analysis

Pair-wise correlations

Deaths per 100,000

Altitude

Latitude

Ethnicity

Mean Vit D

nmol < 30

nmol < 50

nmol < 75

Multivariate regression

Response variable = mean Vit D
Explanatory variables = Deaths per 100,000, Altitude, Latitude, & Ethnicity

## 
## Call:
## lm(formula = mean_vitD ~ Deaths_ht + Alt + Lat + Ethnicity, data = df_mun)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.2271  -3.7962   0.0926   3.3457  17.7142 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 88.8672378  4.0147662  22.135  < 2e-16 ***
## Deaths_ht   -0.0655478  0.0284492  -2.304   0.0227 *  
## Alt         -0.0063961  0.0005499 -11.631  < 2e-16 ***
## Lat         -0.8625039  0.1595556  -5.406 2.62e-07 ***
## Ethnicity   -0.0298645  0.0383426  -0.779   0.4373    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.544 on 144 degrees of freedom
## Multiple R-squared:  0.5678, Adjusted R-squared:  0.5558 
## F-statistic:  47.3 on 4 and 144 DF,  p-value: < 2.2e-16

Explanatory variables, together, explain 30% of the variance in Vit D at municipal scale. When controlling for other variables, each variable shows a negative relation with vit D, but only deaths per 100,000, altitude, and latitude are significant. If ethnicity is removed from the model, results are almost the same in terms of coefficients, their signs, and R2.